PSI - Issue 2_A

L. Bertini et al. / Procedia Structural Integrity 2 (2016) 681–689

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Author name / Structural Integrity Procedia 00 (2016) 000–000

Fig. 3(a) shows the hysteretic loops obtained experimentally at the different cyclic strains then used to obtain the cyclic stress-strain curve of the material. A useful representation of the cyclic stress-strain curve was obtained with the Ramberg-Osgood equation:

n 1

E k           

and the values of K and n are, respectively: 1070 MPa and 0.14. As evident in Fig. 3 (b) the monotonic and the cyclic curves showed very similar trends, thus without any significant hardening of softening. 2.3. Identification of the Chaboche’s hardening model parameters The model considered in the present work is a generalization of the linear kinematic rule introduced by Prager (Prager (1956)), where the yield surface is given by the following function: 0 ) (     Y f X f   (1) Chaboche (1986) and Chaboche et al. (1979) proposed their decomposed hardening rule in the following form:    m i i X X 1 dX C d X dp i i i p i     3 2 Where i C and i  are the couples of material parameter (Chaboche’s parameters), to be identified. The number of parameter couples considered was m=3. Two kinds of experiments were required to perform the identification: one strain controlled hysteresis curve and one stress controlled. In order to find the Chaboche’s parameters three hysteretic loops have been take into account, Fig 3(a): max  = ± 0.5 %, max  = ± 1 % and max  = ± 2 % , plus a stress controlled test at R=-0.66 with 600 max   MPa as shown in Fig. 4.

Fig. 4. Stress controlled test with R=-0.66 and σ max = 600 MPa for the determination of the Chaboche’s parameters.

In this study the yield stress has been used as an extra parameter, thus differentiating the yield stress (engineering, 0.2% offset) obtained from the tensile test. After an optimization calculation, the Chaboche’s parameters obtained from these tests are listed in Tab 4.

Table 4. Chaboche’s parameters.

3 C (MPa)

3 

1 C (MPa)

2 C (MPa)

1 

2 

S’ y0 (MPa)

Parameter

21746

16704

103651

518

7688

6.1

258